The paraboloid meets the x-y plane when x²+y²=9. A circle of radius 3, centre origin.
<span>Use cylindrical coordinates (r,θ,z) so paraboloid becomes z = 9−r² and f = 5r²z. </span>
<span>If F is the mean of f over the region R then F ∫ (R)dV = ∫ (R)fdV </span>
<span>∫ (R)dV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] rdrdθdz </span>
<span>= ∫∫ [θ=0,2π, r=0,3] r(9−r²)drdθ = ∫ [θ=0,2π] { (9/2)3² − (1/4)3⁴} dθ = 81π/2 </span>
<span>∫ (R)fdV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] 5r²z.rdrdθdz </span>
<span>= 5∫∫ [θ=0,2π, r=0,3] ½r³{ (9−r²)² − 0 } drdθ </span>
<span>= (5/2)∫∫ [θ=0,2π, r=0,3] { 81r³ − 18r⁵ + r⁷} drdθ </span>
<span>= (5/2)∫ [θ=0,2π] { (81/4)3⁴− (3)3⁶+ (1/8)3⁸} dθ = 10935π/8 </span>
<span>∴ F = 10935π/8 ÷ 81π/2 = 135/4</span>
Answer:
The answer would be division (B)
Step-by-step explanation:
4x equals the total amount
x equals the cost of one item
Therefore you'd divide total cost by 4 and that would find the cost of one item
Answer:
You are going to get -48
Step-by-step explanation:
For some of the reason, this seemed like multiplication
But anyway, hope this helps, The other person Put down an answer that maybe is incorrect and they posted it like a file like they just don't care like a BOT
Answer: k=1
Step-by-step explanation:
4k-3=-2k+3
take -3 and 3 and add them up on one side and change the sign
4k=-2k+3
+3
4k=-2k+6
take the -2k and change the sign and add to 4k
4k=6
2k
6k=6
now divide both sides with x
6k/6= 6/6
k= 1
